Since the discovery of its transiting nature, the super-Earth 55 Cnc e has become one of the most enthusiastically studied exoplanets, having been observed spectroscopically and photometrically, in the ultraviolet, optical and infrared regimes. To this rapidly growing data set, we contribute 42 days of new, nearly continuous MOST photometry of the 55 Cnc system. Our analysis of these observations together with the discovery photometry obtained in 2011 allows us to determine the planetary radius (1.990+0.084−0.080) and orbital period (0.7365417+0.0000025−0.0000028) of 55 Cnc e with unprecedented precision. We also followed up on the out-of-transit phase variation first observed in the 2011 photometry, and set an upper limit on the depth of the planet's secondary eclipse, leading to an upper limit on its geometric albedo of 0.6.